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arXiv · 1311.7271

On the slope of hyperelliptic fibrations with positive relative irregularity

Xin Lu·Kang Zuo
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Abstract

Let $f:\, S \to B$ be a locally non-trivial relatively minimal fibration of hyperelliptic curves of genus $g\geq 2$ with relative irregularity $q_f$. We show a sharp lower bound on the slope $λ_f$ of $f$. As a consequence, we prove a conjecture of Barja and Stoppino on the lower bound of $λ_f$ as an increasing function of $q_f$ in this case, and we also prove a conjecture of Xiao on the ampleness of the direct image of the relative canonical sheaf if $λ_f<4$.

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Xin Lu, Kang Zuo. 2015-02-11. On the slope of hyperelliptic fibrations with positive relative irregularity. https://arxiv.org/abs/1311.7271

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